Stats on crafted gear are affected by item only in the sense that certain stats/affixes can appear on certain types, at certain levels. For example, only monk gear can get +spirit generation. And low level boots can get +1-2 experience per kill, but a higher level set of boots could get +10.
So to answer the question, yes stats are totally randomly chosen from the pool of affixes available to an item type. There is no bias to make "perfect" items harder to get;it's just statistics that most of what you craft will be mostly useless, like intelligence-dexterity gear, or +health globe/gold pickup radius gear.
The best way to see which affixes an item is eligible for is to look it up on a datamining site. For example, if you are crafting Apprentice Boots from our pal Haedrig, look them up thusly and see their stats list: http://d3db.com/item/i/boots?recipe=205132